4.1 Neural network models

Artificial neural networks (ANNs) are mathematical models that are devised from the need to characterize biological neural processes. As the system of ANNs imitates the way which is used to interact with each other in brain neuron, ANNs are simple and strong processes to interconnect the elements that transmit and process information through electrical impulses. In ANNs, these simple process elements are also known as neurons, and depending on the complexity of the connection schemes, they can develop the ability to describe the nonlinear behavior of many dynamic systems [24]. ANNs are computational models that aim to achieve mathematical formalizations of the brain structure and functions, which are constantly reformed by learning through experience and extracting knowledge from the same experience. In ANNs, the hierarchical structure similar to that in brain is established, where neurons connect with each other and transmit the response to other neurons. Once the ANN's structure is defined, it is necessary to develop memory form experience (experimental data). In order to introduce this experience, the ANN training algorithm performs a weight (ω) fitting process associated with each neuron, such that the actions introduced (input signals) converge to the reactions produced (output signal) [24]. Although ANNs do not provide a physical interpretation of the phenomena that take place in the system, these models can approximate the dynamic behavior of the system, making them suitable universal approximators [22]. ANNs are defined based on three basic characteristics: their architecture, activation functions, and training algorithm. The architecture deals with the type of interconnections between their processing units or neurons, while

the activation function corresponds to the dynamic characteristics of the neuron transfer functions. The training algorithm refers to the parameter fitting procedure, which provides the learning ability.

GBMs take advantage of the well-known mechanistic information through mass and energy balances to describe specific dynamics of the system and expand its

In the determination of bacterial growth kinetic models, GBMs have some advantages compared to BMMs; FFNs are able to describe the system state values, but have important deviations in their estimates, due to their high sensitivity to noise. GBMs combine WBMs with neural network structures, either by feeding the outputs of the ANNs to the state space model, or by backpropagating the estimation error from output layers. Therefore, GBMs offer better forecasting properties and

Monitoring culture media requires the measurement of variables such as biomass concentration, substrates, dissolved oxygen, carbon dioxide, ammonia, and temperature, among others. These values are used for growth kinetics determination and bioreactor design. However, on multiple occasions, implementation of specific sensors is complicated, and there may be limitations in sensing frequency for variables such as biomass concentration. The implementation of indirect measurement methodologies, such as signal filtering, observer design, and ANNs, allows the estimation of some of these variables, and even the estimation of complex variables such as

In control system theory, a major implementation of state observers is a common complementary strategy. These observers estimate some state variables that cannot be easily measured, either by the absence of suitable sensors, or because of low sampling frequency and high delay times. The main types of observers used for these purposes are those based on the Luenberger scheme, finite-dimensional observers, Bayesian estimators such as Kalman filters, interval observers, observers for fault detection, and even models of artificial intelligence such as ANNs and

State observer design requires that the estimated variables are detectable and observable. These states are observable if for a set of specific initial conditions, the internal states of the system are inferred from the knowledge of their outputs. Once its observability is determined, the observer can be designed; the desired type of observer is selected from categories mentioned above. Afterwards, tests of the estimator are carried out by comparing the real values against observer estimates, and in the case of important discrepancies between these values, the observer is

In the case of stirred tank reactors (batch, continuous, or semi-continuous), we may often assume that homogeneous conditions are available, so the system models obtained consist of aggregate parameter systems (ODEs). However, frequently in the case of tubular reactors or solid substrate fermentation systems, homogeneity assumptions are not adequate, so it is necessary to construct using distributed parameter models (PDEs). In the latter case, the design and performance of the main observers, such as Luenberger or Bayesian type, are usually limited, and therefore, it is usual to resort to another type of observer. In such a case, the observers based on a

Soft sensors or virtual sensors are used as state observers in specific application. These soft sensors combine several physical measurements with dynamic charac-

Soft sensors can not only provide variable information to characterize a system

discretized system are substituted for traditional observers [28].

teristics to calculate other variables that are not measured.

but also facilitate the design of the control schemes.

overall microbial growth rate and the heat flux produced by the system.

strengthen their performance in the presence of noise [26].

Fermentation: Metabolism, Kinetic Models, and Bioprocessing

parametric scenario of applicability.

DOI: http://dx.doi.org/10.5772/intechopen.82195

4.3 State observers and soft sensors

hybrid models [27].

19

adjusted or a different one is selected.

Feedforward networks (FNN) represent the simplest network configuration capable of describing the nonlinear behavior of bioreactors. In FFNs, neurons of each layer propagate their information to all neurons in subsequent layers. In each neuron, the input information corresponds to the weighted sum of all the outputs of the previous layer, and the weighting factors, weights and thresholds, are internally fitted for better system description [24].

Another type of ANNs frequently used is recurrent neural networks (RNNs). The structure of RNNs differ from FFNs, in the sense that some of the last layer neuron output signals are fed back as inputs to any previous layer. RNNs could converge to stable system solutions and include the effects of response delays. These characteristics make these models especially useful in the modeling of continuous bioreactors [25].

#### 4.2 Gray box models

BBMs are based on the analysis of data generated to detect correlations, and basic functionalities between the variables and the WBMs are constructed from first principles. A hybrid model category between WBMs and BBMs is GBMs; these models implement a set of tools that combine some of the characteristics of both. Some of these characteristics include properties of process and control design, without losing the ability to explain the phenomena present in the system. Defining a parallel or serial data flow structure allows the integration of both, mechanistic and nonmechanistic information (e.g., Figure 2).

Parallel arrays are mainly used when there is a well-defined mechanistic model of the process and are suitable to improve its estimation performance. It is especially useful in cases where dynamic aspects of the system can be decoupled. Figure 2A shows a conceptual diagram of parallel interaction where the circle represents WBMs and the square BBMs, and the circle inside the square corresponds to a hybrid model. In the case of serial arrays, BBMs describe just specific terms of the WBMs, such as growth kinetics or transport parameters. Figure 2B represents the hybrid model where the BBMs (square) are substituted into the WBMs (circle). Stosch et al. presented a detailed panorama of this model [23].

In the design of bioreactors and their associated controllers, one of the difficulties is the determination of the kinetic model that adequately describes the growth rate of the respective microorganisms. The selection of a kinetic model leads to restrictive models for fixed operating conditions with little extrapolation possibility.

Figure 2. Classification of models as (A) parallel flow nonmechanistic model and (B) serial flow nonmechanistic model.

GBMs take advantage of the well-known mechanistic information through mass and energy balances to describe specific dynamics of the system and expand its parametric scenario of applicability.

In the determination of bacterial growth kinetic models, GBMs have some advantages compared to BMMs; FFNs are able to describe the system state values, but have important deviations in their estimates, due to their high sensitivity to noise. GBMs combine WBMs with neural network structures, either by feeding the outputs of the ANNs to the state space model, or by backpropagating the estimation error from output layers. Therefore, GBMs offer better forecasting properties and strengthen their performance in the presence of noise [26].
